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The Riemann¿Hilbert approach to strong asymptotics for orthogonal polynomials on [-1,1]
Abstract We consider polynomials that are orthogonal on [−1,1] with respect to a modified Jacobi weight (1− x ) α (1+ x ) β h ( x ), with α , β >−1 and h real analytic and strictly positive onExpand
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The Asymptotic Zero Distribution of Orthogonal Polynomials with Varying Recurrence Coefficients
We study the zeros of orthogonal polynomials pn, N, n=0, 1, ?, that are generated by recurrence coefficients an, N and bn, N depending on a parameter N. Assuming that the recurrence coefficientsExpand
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Starting from a sequence {pn{x; no)} of orthogonal polynomials with an orthogonality measure yurj supported on Eo C (—1,1), we construct a new sequence {p"(x;fi)} of orthogonal polynomials on£ =Expand
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Orthogonal matrix polynomials and higher-order recurrence relations
Abstract It is well known that orthogonal polynomials on the real line satisfy a three-term recurrence relation and conversely every system of polynomials satisfying a three-term recurrence relationExpand
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Asymptotics for Orthogonal Polynomials
Orthogonal polynomials on a compact set.- Asymptotically periodic recurrence coefficients.- Probabilistic proofs of asymptotic formulas.- Orthogonal polynomials on unbounded sets.- Zero distributionExpand
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Some classical multiple orthogonal polynomials
Recently there has been a renewed interest in an extension of the notion of orthogonal polynomials known as multiple orthogonal polynomials. This notion comes from simultaneous rational approximationExpand
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Orthogonal matrix polynomials and applications
Orthogonal matrix polynomials, on the real line or on the unit circle, have properties which are natural generalizations of properties of scalar orthogonal polynomials, appropriately modified for theExpand
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Riemann-Hilbert Problems for Multiple Orthogonal Polynomials
In the early nineties, Fokas, Its and Kitaev observed that there is a natural Riemann-Hilbert problem (for 2 x×2 matrix functions) associated with a system of orthogonal polynomials. ThisExpand
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Perturbation of Orthogonal Polynomials on an Arc of the Unit Circle, II
Orthogonal polynomials on the unit circle are fully determined by their reflection coefficients through the Szego? recurrences. Assuming that the reflection coefficients converge to a complexExpand
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